ApCoCoA:CharP.GBasisF8

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Char2.GBasisF8

computing a gbasis of a given ideal in <formula>\mathbb{F}_{8}</formula>

Syntax

$char2.GBasisF8(Ideal):List

Description


This command computes a Groebner basis in the field <formula> \mathbb{F}_{8} = (/mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^3 + x +1)}</formula>. It uses the ApCoCoA Server and the ApCoCoALib's class RingF8.

The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 7 represent the field's elements. Details on this representation can be found here. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g.

<formula> 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0</formula>

So the number <formula>11</formula> corresponds to the polynomial <formula>x^3 + x + 1</formula>.


See also

ApCoCoA:GBasis

ApCoCoA:char2.GBasisF2

ApCoCoA:char2.GBasisF4

ApCoCoA:char2.GBasisF16

ApCoCoA:char2.GBasisF32

ApCoCoA:char2.GBasisF64

ApCoCoA:char2.GBasisF128

ApCoCoA:char2.GBasisF256

ApCoCoA:char2.GBasisF512

ApCoCoA:char2.GBasisF1024

ApCoCoA:char2.GBasisF2048

ApCoCoA:char2.GBasisF4096

ApCoCoA:char2.GBasisModSquares